123abondA: dollars \(\in \mathbb{R}\) to invest in bond A
bondB: dollars \(\in \mathbb{R}\) to invest in bond B
bondC: dollars \(\in \mathbb{R}\) to invest in bond C
bondD: dollars \(\in \mathbb{R}\) to invest in bond D
bondE: dollars \(\in \mathbb{R}\) to invest in bond E
\[ Maximize \ Z = (0.043 \times bondA) + (0.027 \times bondB) + (0.025 \times bondC) + (0.022 \times bondD) + (0.045 \times bondE) \]
C1: Budget to invest is $10 MM or less \[ budget: bondA + bondB + bondC + bondD + bondE \leq 10 \]
C2: At least $4 million must be invested in government and agency bonds \[ govtAndAgency: bondB + bondC + bondD \geq 4 \]
C3: Average Quality of the Portfolio must not exceed 1.4 \[ avgQuality: (0.6 \times bondA) + (0.6 \times bondB) - (0.4 \times bondC) - (0.4 \times bondD) + (3.6 \times bondE) \leq 0 \]
C4: The Average Maturity must not Exceed Five Years \[ avgMaturity: (4 \times bondA) + (10 \times bondB) - (1 \times bondC) - (2 \times bondD) - (3 \times bondE) \leq 0 \]
4atv = the number of minutes \(\in \mathbb{R}\) to air advertising on the television medium
magazine = the number of pages \(\in \mathbb{I}\) to to advertise on the magazine medium
\[ Maximize \ Z = (1.8\times tv) + (1.0 \times magazine) \]
C1: Must not Exceed Budget of 1 Million dollars
\[
budget: (20,000 \times tv) + (10,000 \times magazine) \leq 1,000,000
\]
C2: Must have at least 10 minutes of air time on the TV medium
\[
minTimeTV: tv \geq 10
\]
4(a) Graphically by HandbC3: Only 100 person weeks available, given it takes three weeks and one week to create a tv and magazine minute for advertisement, respectively.
\[
personWeeks: (3 \times tv) + (1 \times magazine) \leq 100
\]
ctv = the number of minutes \(\in \mathbb{R}\) to air advertising on the television medium
magazine = the number of pages \(\in \mathbb{I}\) to to advertise on the magazine medium radio = the number of minutes \(\in \mathbb{R}\) to air advertising on the radio medium
\[ Maximize \ Z = (1.80\times tv) + (1.00 \times magazine) + (0.25 \times radio) \]
C1: Must not Exceed Budget of 1 Million dollars \[ budget: (20,000 \times tv) + (10,000 \times magazine) + (2,000 \times radio) \leq 1,000,000 \]
C2: Must have at least 10 minutes of air time on the TV medium
\[
minTimeTV: tv \geq 10
\]
C3: Only 100 person weeks available, given it takes three weeks and one week to create a tv and magazine minute for advertisement, respectively. It only takes one day for radio.
\[
personWeeks: (3 \times tv) + (1 \times magazine) + (\frac{1}{7} \times radio) \leq 100
\]
dC4: Must sign up for at least 2 magazine pages \[ minMagazines: magazine \geq 2 \]
C5: Must to exceed 120 minutes of radio \[ maxRadio: radio \leq 120 \]
5.mod and Input Data .dataThere is no difference in the optimal solution because the range of Time before there is a change in optimal remains the same, and the hours available have not changed.
b\[ totalWeight: \sum_{p \ \in \ PROD} Make_{p} \leq max\_weight \]
The total number of tons has reduced from 7,000 to 6,500 per week
c\[ maximize \ Total\_Tons = \sum_{p \ \in \ PROD} Make_{p} \]
The data file does not make a diference in the optimal (assuming that is what the question is asking). Please note that the total number of tons produced are the same as in the
basemodel; however, the allocation of tons have shifted among each of the products.
de.dat File6a - cbondA: dollars \(\in \mathbb{R}\) to invest in bond A
bondB: dollars \(\in \mathbb{R}\) to invest in bond B
bondC: dollars \(\in \mathbb{R}\) to invest in bond C
bondD: dollars \(\in \mathbb{R}\) to invest in bond D
bondE: dollars \(\in \mathbb{R}\) to invest in bond E
\[ Maximize \ Z = (0.043 \times bondA) + (0.027 \times bondB) + (0.025 \times bondC) + (0.022 \times bondD) + (0.045 \times bondE) \]
C1: Budget to invest is $10 MM or less \[ budget: bondA + bondB + bondC + bondD + bondE \leq 10 \]
C2: At least $4 million must be invested in government and agency bonds \[ govtAndAgency: bondB + bondC + bondD \geq 4 \]
C3: Average Quality of the Portfolio must not exceed 1.4 \[ avgQuality: (0.6 \times bondA) + (0.6 \times bondB) - (0.4 \times bondC) - (0.4 \times bondD) + (3.6 \times bondE) \leq 0 \]
C4: The Average Maturity must not Exceed Five Years \[ avgMaturity: (4 \times bondA) + (10 \times bondB) - (1 \times bondC) - (2 \times bondD) - (3 \times bondE) \leq 0 \]
C5: Only select Bonds A and D (Don’t select B, C, or E) \[ onlyAandB: bondB + bondC + bondE = 0; \]
C6: Municipal Bonds must be less than or equal to $3 MM \[ municipal: bondA \leq 3; \]
d:You may not borrow more than 2.83%, since that is the expected
yield to maturity (30% of bondA * 4.3%) + (70% of bondD * 2.2%)
e:If you borrowed at a rate greater than the expected YTM, then the
venture would not be profitable.